Occasional reflections on Life, the World, and Mathematics

The BBC reports on a study by the Prisoners Education Trust, of the impact of the recent decision of the prison service to limit prisoners’ access to books. The Ministry of Justice has dismissed the study, saying

the PET survey of 343 inmates represented just 0.01% of the total prison population in England and Wales.

This is a twofer, with a pair of errors packed into impressively small space. Even a government minister should be able to calculate that if 343 inmates represent 0.01% of the prison population, then more than 6% of the population (53.5 million) must be imprisoned, which I don’t need to check the figures to know must be wrong. But I did check it, and find that the Ministry of Justice made a wee error of not quite 2 orders of magnitude. According to this publication (coincidentally, also from the Ministry of Justice) there were about 84,000 prisoners in June 2013. Assuming there haven’t been any huge changes since then, those 343 inmates in fact represent 0.4% of the prison population. Where is Michael Gove when you need him?

More generally, the comment conveyed the impression that if the sample were a small fraction of the population then it couldn’t be statistically valid. Of course, that’s not true. If you were doing an election poll of the whole population of England, a random sample of 0.01% of the population would be about 5000 people, which is much larger than most surveys, and enough to get a result that’s accurate to within about ± 1.5%. The real problem with this survey is that it’s not a random sample, and not representative, being self-selected among readers of a certain magazine; but there is no pretence about that, and if the Ministry of Justice were interested in addressing the issue rather than issuing talking points, they could address the question of whether the concerns raised by the more literate of the prisoner population most concerned with literacy are worth taking seriously.